Communication system, base station, and mobile station

ABSTRACT

A communication system includes mobile stations carrying out transmission at report cycles selected from a group consisting of 0, 1 and other integers without having a relation of a multiple and including a lot of prime numbers.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of co-pending U.S. patent applicationSer. No. 10/507,519, filed Sep. 14, 2004, which claims priority toPCT/JP02/04588, filed May 10, 2002, the entire contents of which ishereby incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a communication system, base station,and mobile station of mobile communications for carrying out high-speedradio data communication.

BACKGROUND ART

A plurality of communication schemes called a third generation areadopted as IMT-2000 by ITU (International Telecommunication Union) asmobile radio communication schemes typified by mobile telephones. Amongthem, W-CDMA (Wideband Code Division Multiple Access) was put intocommercial service in Japan in 2001.

The W-CDMA scheme aims to achieve a communication rate of about 2 Mbps(megabits per second) per mobile station at the maximum. The firstspecification was decided and published by 3GPP (Third-GenerationPartnership Project; http://www.3gpp.org), one of the standardizationgroups, as Release 1999, a version standardized in 1999. Incidentally,as a detailed manual of the W-CDMA FDD schemes in general, “W-CDMAmobile communication system”, supervised by Keiji Tachikawa, MaruzenCo., Ltd. is known.

FIG. 1 is a schematic diagram showing a conventional communicationsystem based on the W-CDMA scheme. In FIG. 1, the reference numeral 1designates a base station (BS), 2 designates a mobile station (MS) thatcarries out radio communication with the base station 1, 3 designates adownlink, 3 a designates a channel (dedicated channel) assigned to themobile station individually among the downlink 3 used by the basestation 1 for transmitting data to the mobile station 2, 3 b designatesa channel (shared channel) transmitted to a plurality of mobile stationsin common among the downlink 3, and 4 designates an uplink (dedicatedchannel) used by the mobile station 2 for transmitting data to the basestation 1.

The W-CDMA is divided into FDD (Frequency Division Duplex) that assignsdifferent radio frequencies to downlink 3 and uplink 4, and TDD (TimeDivision Duplex) that utilizes the same radio frequency and separatesthe downlink 3 and uplink 4 on a time division basis. Here, the FDD willbe described.

Next, the operation will be described.

The downlink 3 a consists of a DPDCH (Dedicated Physical Data CHannel),a data channel, and a DPCCH (Dedicated Physical Control CHannel), acontrol channel. Both the channels are time division multiplexed andtransmitted.

The downlink 3 b is a CPICH (Common Pilot CHannel) for transmitting apilot signal for the mobile station 2 to establish synchronization withthe base station 1.

The downlink 3 a and downlink 3 b are multiplied by spreading codesdifferent for individual transmission data to separate the channels,followed by multiplication of a base station identification code (theso-called scramble code) assigned to the base station 1 to betransmitted.

The uplink 4 consists of a DPDCH (Dedicated Physical Data CHannel), adata channel, and a DPCCH (Dedicated Physical Control CHannel), acontrol channel, which are transmitted after undergoing IQ multiplexing.

The uplink 4 is multiplied by spreading codes different for individualtransmission data to separate the channels, followed by the IQmultiplexing, and by multiplication by a mobile station identificationcode (the so-called scramble code) assigned to the mobile station 2 tobe transmitted.

Recently, a large volume packet data transmission method has becomepopular in which a transmission rate of the downlink 3 is higher thanthat of the uplink 4, which is typified by the utilization of theInternet. To further increase the rate of the downlink data to betransmitted from the base station 1 to the mobile station 2 in thismethod, HSDPA (High Speed Downlink Packet Access), in which exclusivedownlink for high-speed packet transmission is to be added, has beenproposed and studied (see “High Speed Downlink Packet Access: PhysicalLayer Aspects (Release 5)” of 3GPP specification TR25.858 v5.0.0(2002-03)). FIG. 2 is a diagram showing a configuration of the HSDPA. InFIG. 2, the reference numeral 5 designates an exclusive downlink for thehigh-speed packet transmission, and 6 designates an uplink. Theremaining components are the same as those of FIG. 1.

Next, the operation will be described.

The downlink 5, which is transmitted using a so-called shared channelcommon to a plurality of mobile stations, is divided into a HS-DSCH(High Speed-Downlink Shared CHannel), a data channel, and a HS-SCCH(High Speed-Shared Control CHannel), a control channel.

It has been decided that the HS-DSCH employs AMC (Adaptive Modulationand Coding) that can adaptively vary a modulation scheme (such as QPSKand 16 QAM) and an error-correcting coding rate in accordance with adownlink environment (quality). In addition, because of packettransmission, retransmission control (ARQ: Auto Repeat reQuest) iscarried out for reception error.

Furthermore, both the channels (HS-DSCH and HS-SCCH) are subjected tochannel separation and base station identification just as the otherdownlinks (downlinks 3 a and 3 b).

In addition, to add the new downlink 5, it has been studied that themobile station 2 transmits, to the base station 1, response data(ACK/NACK) corresponding to the downlink high-speed packet data, anddownlink quality information (QI: Quality Indicator). To transmit theresponse data, a dedicated individual control channel (uplink 6) isadded as shown in FIG. 2.

As for the uplink 6, it has been studied to separate and identify thechannel using a spreading code for channel separation in the same manneras the conventional uplink channel, followed by carrying out additionalIQ multiplexing to the conventional uplink 4. In TR25.858, the dedicatedcontrol channel is referred to as “HS-DPCCH” (High-Speed-DedicatedPhysical Control CHannel).

As for the ACK/NACK, it has been studied to transmit from the mobilestation 2 only when data is transmitted from the base station 1 throughthe downlink 5, and is not transmitted unless a packet is transmitted.As for the QI, it is studied to transmit it from the mobile station 2 tothe base station 1 periodically. Accordingly, the transmissions areperformed independently.

The transmission cycle and timing offset of the QI is specified by thebase station 1 as parameters in advance, and their values (report cyclek, and offset) are defined in TR25.858. The values and ranges of thesevalues, however, are provisional values for discussion, and have not yetbeen determined. The provisional values of the k are 0, 1, 5, 10, 20,40, and 80, and the ranges of the offset for each k can take values of0≦offset≦k−1. Since the k and offset are parameters, they can be alteredhalfway through the communication in accordance with a variable rate ofthe downlink environment.

FIG. 3 is a diagram illustrating a format of the HS-DPCCH, which will bedescribed below.

It has been studied to separate the ACK/NACK data field from the QI datafield in time, and to assign the QI twice the time assigned to theACK/NACK. The combination of the two data is specified in terms of atime unit (Subframe) of 2 ms. The Subframe is also a transmission unitof the HSDPA downlink 5.

The report cycle k and offset are represented in terms of the Subframeused as the unit.

FIG. 4 is a diagram illustrating transmission timing of the QIexcerpted. FIG. 4 illustrates an example including three mobile stations(MS's) to which the report cycle k=5 is assigned and one mobile station(MS) to which k=1 is assigned. The mobile stations with k=5 are assigneddifferent offsets (=0, 1 and 2). In contrast, the mobile station withk=1 is assigned the offset=0, which means that the transmission iscarried out consecutively because the report cycle is one.

Although the report cycle k is assumed to be one of 0, 1, 5, 10, 20, 40,and 80 at the present, their evidence is not cited. It is assumed thatk=0 indicates no transmission.

FIG. 5 is a conceived internal block diagram of a base station enablingthe HSDPA, and FIG. 6 is a conceived internal block diagram of a mobilestation enabling the HSDPA. In FIG. 5, reference numerals 200 a, 200 band 200 c each designate a spreader, and 201 a, 201 b and 201 c eachdesignate a scrambler. The reference numeral 202 designates an adder,203 designates a (transmitting) frequency converter, 204 designates atransmitting/receiving antenna, and 205 designates an ARQ controller forcarrying out AMC operation and retransmission timing control. Thereference numeral 206 designates a (receiving) frequency converter, and207 designates a descrambler. Reference numerals 208 a and 208 b eachdesignate a despreader, the reference numeral 209 designates a (time)divider, 210 designates a table for selecting an MCS from the QI, and211 designates an MCS controller. The MCS will be described later.

In FIG. 6, reference numerals 300 a and 300 b each designate a spreaderand 301 a and 301 b each designate a scrambler. The reference numeral302 designates an adder, 303 designates a (transmitting) frequencyconverter, 304 designates a transmitting/receiving antenna, and 305designates a (time) combiner. The reference numeral 306 designates a(receiving) frequency converter, and 307 designates a descrambler.Reference numerals 308 a, 308 b and 308 c each designate a despreader.The reference numeral 309 designates a QI transmission controller, 310designates a converter, 311 designates a QI transmission timingcontroller, 312 designates a data decision circuit, and 313 designatesan ACK/NACK transmission timing controller.

In FIGS. 5 and 6, the parameters (k and offset) for determining the QItransmission timing are assumed to be transmitted as part of the DPDCH,the conventional data channel, and informed to the mobile station. Inaddition, as a downlink quality evaluation method, a method is assumedof using the SN ratio of the CPICH estimated by the mobile station. Thisis because the CPICH is always transmitted at a constant transmit power,which enables the evaluation of the downlink quality.

Next, the transmitting operation from the base station and the receivingoperation in the base station will be described.

The data of the CPICH, a shared channel, and the data of theDPDCH/DPCCH, individual channels, are spread by the individual spreaders200 a and 200 b using the different channel spreading codes according tothe well-known common technique, followed by being multiplied by themobile station identification code (scramble code) at the scramblers 201a and 201 b according to the well-known common technique, and are inputto the adder 202.

On the other hand, the data of the HS-DSCH/HS-SCCH, the channels for theHSDPA, are supplied to the ARQ controller 205 to undergo thetransmission timing control. This is because the HSDPA channel is ashared channel for transmitting the downlink to a plurality of mobilestations, and transmits packet data. The output of the ARQ controller205 is spread by the spreader 200 c according to the well-known commontechnique, is multiplied by the mobile station identification code atthe scrambler 201 c according to the well-known common technique, and issupplied to the adder 202.

The data summed up by the adder 202, the so-called baseband frequencysignal, is converted to a radio frequency signal by the (transmitting)frequency converter 203 according to the well-known common technique,and is transmitted from the transmitting/receiving antenna 204 to themobile station as the downlink.

On the other hand, the radio frequency signal received from the mobilestation by the transmitting/receiving antenna 204 is converted to abaseband signal by the (receiving) frequency converter 206 according tothe well-known common technique. The baseband signal is multiplied bythe scramble code, the identification number of the mobile stationreceived, at the descrambler 207 according to the well-known commontechnique.

The HS-DPCCH is despread by the despreader 208 a according to thewell-known common technique, and is extracted as the originaltransmission data to be divided to the ACK/NACK data and QI informationdata by the (time) divider 209. The ACK/NACK data, the packet response,is supplied to the ARQ controller 205 to undergo the retransmission andtiming control in accordance with the response.

The QI data separated by the (time) divider 209 is converted to the MCS(Modulation & Coding Scheme) information for packet transmissioncorresponding to the downlink quality (QI) by the table 210. The MCSinformation output from the table 210 is supplied to the MCS controller211. The MCS controller 211 supplies the ARQ controller 205 with asignal for controlling the AMC operation, thereby carrying out the AMCoperation.

The DPDCH/DPCCH, the conventional uplink channels, are despread by thedespreader 208 b, and are restored to the original transmission data.

Next, the operation of the mobile station will be described withreference to FIG. 6.

First, the transmitting operation of the mobile station will bedescribed, and then the receiving operation of the mobile station willbe described.

The data of the DPDCH/DPCCH, the conventional channels transmitted fromthe mobile station, is spread by the spreader 300 a using the channelseparating spreading code according to the well-known common technique,is multiplied by the mobile station identification code at the scrambler301 a according to the well-known common technique, and is supplied tothe adder 302.

As for the data (ACK/NACK and QI) of the HS-DPCCH, the HSDPA channel, ifany transmission data is present, it is time division multiplexed by the(time) combiner 305 in accordance with the format. Then, the data isspread by the spreader 300 b using the channel spreading code accordingto the well-known common technique, is multiplied by the mobile stationidentification code at the scrambler 301 b according to the well-knowncommon technique, and is supplied to the adder 302.

The adder 302 sums up the outputs of the scramblers 301 a and 301 b. Theoutput of the adder 302, the so-called baseband frequency signal, isconverted to the radio frequency signal by the (transmitting) frequencyconverter 303 according to the well-known common technique, and istransmitted from the transmitting/receiving antenna 304 to the basestation via the uplink.

On the other hand, the radio frequency signal from the base stationreceived by the transmitting/receiving antenna 304 is converted to abaseband signal by the (receiving) frequency converter 306 according tothe well-known common technique. The baseband signal is multiplied bythe scramble code, the identification number of the base stationreceived, at the descrambler 307 according to the well-known commontechnique.

As for the DPDCH/DPCCH, which are the conventional channels, they aredespread by the despreader 308 a according to the well-known commontechnique, and are extracted as the original data. At the same time,they are supplied to the QI transmission controller 309 that extractsand holds the QI transmission parameters.

The CPICH, the shared channel, is despread by the despreader 308 baccording to the well-known common technique. The converter 310calculates the SN ratio of the CPICH from the output of the despreader308 b to generate the QI information data to be transmitted. The QIinformation data is transmitted as the HS-DPCCH under the timing controlof the QI transmission timing controller 311 according to the parametersof the QI transmission controller 309.

As an example of the correspondence between the SN ratio of the CPICHand the QI information data, the relation as shown in Table 1 isspecified in a standard in advance. This make is possible for the basestation and mobile station to transmit and receive AMC controlled datausing only the QI data.

TABLE 1 QI SN ratio transmission modulation scheme, transmission (dB)data encoding ratio rate (bps) −10 1 QPSK, ⅓ 3M −5 2 QPSK, ½ 5M 0 316QAM, ⅓ 7M 5 4 16QAM, ½ 10M 

The HS-SDCH/HS-SCCH, the channels for the HSDPA, are despread by thedespreader 308 c to extract the data according to the well-known commontechnique. The data decision circuit 312 decides the presence or absenceof an error of the extracted packet data, and generates the ACK when theerror is absent, and the NACK if the error is present. The ACK/NACK dataundergoes the timing control by the ACK/NACK transmission timingcontroller 313, and is transmitted as the HS-DPCCH.

FIG. 7 is a diagram illustrating an example of the QI transmissiontiming of the conventional communication system.

FIG. 7 illustrates individual QI transmission states of the systemincluding three mobile stations with k=5 and different offsets(offsets=0, 1, 2), and one mobile station with k=10 and offset=0.

The values k and offsets can vary from mobile station to mobile stationbecause the base station notifies the mobile stations of differentvalues depending on the changing environment and quality of thedownlinks to the mobile stations.

When the mobile stations with different k are present in the system, andif the values k have a relation of a multiple such as 5 and 10, theprobability of coincidence of the transmission timing increases for acombination of particular mobile stations depending on the manner ofassigning the offset (in FIG. 7, the two mobile stations (MS#1 and MS#4)with the offset=0 have the coincidence).

In addition, if these mobile stations are close to each other, theinterference between the mobile stations can be increased.

With the foregoing configuration, the conventional communication systemhas a problem of causing interference because the QI transmission cycleparameters (other than 0 or 1) can take values having the relation of amultiple.

The present invention is implemented to solve the foregoing problem.Therefore it is an object of the present invention to provide acommunication system capable of reducing the probability of transmissioncollision in a combination of particular mobile stations, and reducingthe interference between the mobile stations in the communicationsystem, in which the mobile stations report the downlink qualityinformation at alterable report cycles.

DISCLOSURE OF THE INVENTION

According to an aspect of the present invention, there is provided acommunication system in which mobile stations transmit to a base stationquality information about a downlink from the base station to the mobilestations at alterable report cycles, the communication system includinga channel that varies a transmission rate by changing a transmissionformat of data transmitted from the base station through the downlink inresponse to the quality information transmitted, wherein the individualreport cycles of the mobile stations are selected from a groupconsisting of 0, 1 and at least two positive integers without having arelation of a multiple, and of at least zero positive integer greaterthan the at least two positive integers without having the relation of amultiple.

Thus it offers an advantage of being able to reduce the transmissioncollision probability in a combination of particular mobile stations,and to reduce the interference between the mobile stations.

In the communication system, the at least two positive integers withouthaving the relation of a multiple can be prime numbers.

Thus it offers an advantage of being able to reduce the transmissioncollision probability in a combination of particular mobile stations,and to reduce the interference between the mobile stations.

According to another object of the present invention, there is provideda communication system in which mobile stations transmit to a basestation quality information about a downlink from the base station tothe mobile stations at alterable report cycles, the communication systemincluding a channel that varies a transmission rate by changing atransmission format of data transmitted from the base station throughthe downlink in response to the quality information transmitted, whereinthe individual report cycles of the mobile stations are selected from agroup consisting of 0, 1 and positive integers equal to or greater thantwo, where the maximum value of the positive integers differs from aleast common multiple of any two integers of the positive integers otherthan the maximum value.

Thus it offers an advantage of being able to reduce the collisionprobability up to the maximum k value.

In the communication system, the maximum value can be less than theleast common multiple.

Thus the collision report cycle of the two mobile stations becomesgreater than the maximum value of k, thereby offering an advantage ofbeing able to reduce the probability of the collision between the QItransmission.

According to still another aspect of the present invention, there isprovided a communication system in which mobile stations transmit to abase station quality information about a downlink from the base stationto the mobile stations at alterable report cycles, the communicationsystem including a channel that varies a transmission rate by changing atransmission format of data transmitted from the base station throughthe downlink in response to the quality information transmitted, whereinthe individual report cycles of the mobile stations are selected from agroup consisting of 0, 1 and positive integers equal to or greater thantwo, where larger values of the positive integers are obtained fromsmaller values of the positive integers.

Thus it offers an advantage of being able to reduce the probability ofthe collision between the QI transmission of particular mobile stations,and to eliminate the need for storing all the possible numbers of k inthe base station when there are many k values.

According to still another aspect of the present invention, there isprovided a communication system in which mobile stations transmit tobase stations quality information about downlinks from the base stationsto the mobile stations at alterable report cycles, the communicationsystem including channels each varying a transmission rate by changing atransmission format of data transmitted from the base stations throughthe downlinks in response to the quality information transmitted,wherein the base stations each receive the quality information from themobile stations at the report cycles whose possible values differ fromeach other.

Thus it offers an advantage of being able to reduce the probability ofthe collision between the QI transmission, and to reduce theinterference between the mobile stations at the same time.

In the communication system, the base stations can each exchange thereport cycles, at which the base stations receive the qualityinformation from the mobile stations, via an inter-base stationcommunication line interconnecting the base stations.

Thus using the different groups of k offers an advantage of being ableto reduce the probability of the collision between the QI transmission,and to reduce the interference between the mobile stations at the sametime.

According to still another aspect of the present invention, there isprovided a base station characterized by selecting report cycles, atwhich mobile stations transmit to the base station quality informationabout a downlink from the base station to the mobile stations, fromcandidates having a plurality of report cycles including at least tworeport cycles without having a relation of a multiple, and by notifyingthe mobile stations of the report cycles selected.

Thus it offers an advantage of being able to reduce the transmissioncollision probability in a combination of particular mobile stations,and to reduce the interference between the mobile stations.

According to still another aspect of the present invention, there isprovided a mobile station characterized by transmitting to a basestation quality information about a downlink from the base station tothe mobile station with switching at least two report cycles withouthaving a relation of a multiple.

Thus it offers an advantage of being able to reduce the transmissioncollision probability in a combination of particular mobile stations,and to reduce the interference between the mobile stations.

In the mobile station, the at least two report cycles without having therelation of a multiple can be each n times a unit report cycle, where nis a positive integer equal to or greater than two.

Thus it offers an advantage of being able to reduce the transmissioncollision probability in a combination of particular mobile stations,and to reduce the interference between the mobile stations.

In the mobile station, the base station can change, in response to thequality information, a modulation scheme of a data channel used inconjunction with a DPDCH in a downlink.

Thus it offers an advantage of being able to reduce the transmissioncollision probability in a combination of particular mobile stations,and to reduce the interference between the mobile stations.

In the mobile station, the base station can change, in response to thequality information, an error correcting encoding ratio of a datachannel used in conjunction with a DPDCH in a downlink.

Thus it offers an advantage of being able to reduce the transmissioncollision probability in a combination of particular mobile stations,and to reduce the interference between the mobile stations.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing a configuration of a conventionalcommunication system;

FIG. 2 is a diagram showing a configuration of HSDPA;

FIG. 3 is a diagram showing a format of a HS-DPCCH;

FIG. 4 is a diagram showing QI transmission timing excerpted in part;

FIG. 5 is a conceived internal block diagram of a base station capableof carrying out the HSDPA;

FIG. 6 is a conceived internal block diagram of a mobile station capableof carrying out the HSDPA;

FIG. 7 is a diagram showing QI transmission timing of a conventionalcommunication system;

FIG. 8 is a diagram showing an example of the QI transmission timing ofa communication system of an embodiment 1 in accordance with the presentinvention; and

FIG. 9 is a diagram showing a communication system of an embodiment 4 inaccordance with the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

The best mode for carrying out the invention will now be described withreference to the accompanying drawings to explain the present inventionin more detail.

Embodiment 1

FIG. 8 is a diagram showing an example of the QI transmission timing ofa communication system of an embodiment 1 in accordance with the presentinvention. It is assumed here that k is specified to take values kε{0,1, 5, 11, 19, 41, 83, 161}. FIG. 8 shows a case where three mobilestations with k=5 and different offsets (0, 1, 2) and one mobile stationwith k=11 and offset=0 each carry out the QI transmission. In contrastwith this, in FIG. 7, which shows an example of the QI transmissiontiming of a conventional communication system, three mobile stationswith k=5 and different offsets (0, 1, 2) and one mobile station withk=10 and offset=0 each carry out the QI transmission.

The communication system of the embodiment 1 can have the sameconfiguration of the HSDPA as shown in FIG. 2.

Next, the operation will be described.

In the present embodiment 1, the mobile stations with different k selecttheir k not from the numbers having the relation of a multiple, but fromthe allowed numbers of k consisting of prime numbers such as 5 and 11.Accordingly, the report cycle that causes the transmission collision(the least common multiple of the two k's 5 and 11) becomes 55, which islonger than 10, the report cycle of the conventional communicationsystem, that is, the least common multiple of 5 and 10. Thus, thecollision probability reduces, and the combinations of the mobilestations causing the collision vary with time. As a result, theprobability of coincidence of transmission timing at a particularcombination of the mobile stations also reduces.

Incidentally, although the present embodiment 1 employs the numbersselected from prime numbers as the possible numbers of k other than 0and 1, this is not essential. For example, even numbers are alsoavailable unless they have the relation of a multiple such as k={0, 1,4, 10, 22, . . . }. This offers an advantage of being able to broadenthe options of the base station of selecting the values k.

In addition, although the present embodiment 1 employs the numbersselected from prime numbers as the possible numbers of k other than 0and 1, when the values k are large, the collision probability is smallfrom the beginning. Thus the problem arises when k takes small values.Accordingly, it is not necessary to select all the k values from primenumbers. It is obvious that the substantially same advantage can beachieved by selecting small k values from prime numbers, and byassigning the same values as the conventional values to large k values.

As described above, the communication system of the present embodiment 1is configured such that the mobile stations (2) transmit to the basestation (1) the quality information (QI) about the downlink (3) from thebase station (1) to the mobile stations (2) at alterable report cycles(k), and the communication system includes the channel (5) that variesthe transmission rate by changing the transmission format of the datatransmitted from the base station (1) through the downlink (3) accordingto the quality information (QI) transmitted, wherein the individualreport cycles (k) of the mobile stations (2) are selected from a groupconsisting of 0, 1 and at least two positive integers without having therelation of a multiple, and of at least zero positive integers greaterthan the at least two positive integers without having the relation of amultiple.

In the communication system of the present embodiment 1, the at leasttwo positive integers without having the relation of a multiple areprime numbers.

Although the embodiment 1 is described by way of example of thecommunication system, the embodiment 1 can be implemented in the form ofone of the base station and mobile station constituting thecommunication system.

The base station of the present embodiment 1 selects the report cycles(k), at which the mobile stations (2) transmit to the base station (1)the quality information (QI) about the downlink (3) from the basestation (1) to the mobile stations (2), from the candidates having aplurality of report cycles including at least two report cycles withouthaving the relation of a multiple, and instructs the mobile stations (2)on the report cycles selected.

The mobile station of the present embodiment 1 can transmit to the basestation (1) the quality information (QI) about the downlink (3) from thebase station (1) to the mobile stations (2) with switching at least tworeport cycles (k) without having the relation of a multiple.

In the mobile station of the present embodiment 1, the at least tworeport cycles without having the relation of a multiple are each n timesa unit report cycle (k=1), where n is a positive integer equal to orgreater than two.

As for the mobile station of the present embodiment 1, according to thequality information (QI), the base station (1) changes the modulationscheme of the data channel which is used in conjunction with the DPDCHin the downlink (3).

As for the mobile station of the present embodiment 1, according to thequality information (QI), the base station (1) changes the errorcorrecting encoding ratio of the data channel which is used inconjunction with the DPDCH in the downlink (3).

As is clear from the description above, according to the presentembodiment 1, the report cycles k of the mobile stations in thecombination of particular mobile stations are determined at valueswithout having the relation of a multiple. As a result, the presentembodiment 1 offers an advantage of being able to reduce thetransmission collision probability in the combination of the particularmobile stations, and to reduce the interference between the mobilestations.

According to the present embodiment 1, the report cycles k of the mobilestations in the combination of particular mobile stations are primenumbers without having the relation of a multiple. As a result, thepresent embodiment 1 offers an advantage of being able to reduce thetransmission collision probability in the combination of the particularmobile stations, and to reduce the interference between the mobilestations.

According to the present embodiment 1, the base station selects thereport cycles, at which the mobile stations transmit to the base stationthe quality information about the downlink from the base station to themobile stations, from the candidates having a plurality of report cyclesincluding at least two report cycles without having the relation of amultiple, and notifies the mobile stations of the report cyclesselected. As a result, the present embodiment 1 offers an advantage ofbeing able to reduce the transmission collision probability in thecombination of the particular mobile stations, and to reduce theinterference between the mobile stations.

According to the present embodiment 1, the mobile station can transmitto the base station the quality information about the downlink from thebase station to the mobile station with switching at least two reportcycles without having the relation of a multiple. As a result, thepresent embodiment 1 offers an advantage of being able to reduce thetransmission collision probability in the combination of the particularmobile stations, and to reduce the interference between the mobilestations.

According to the present embodiment 1, the at least two report cycleswithout having the relation of a multiple are each n times a unit reportcycle, where n is a positive integer equal to or greater than two. As aresult, the present embodiment 1 offers an advantage of being able toreduce the transmission collision probability in the combination of theparticular mobile stations, and to reduce the interference between themobile stations.

According to the present embodiment 1, the base station changes themodulation scheme of the data channel, which is used in conjunction withthe DPDCH in the downlink, in accordance with the quality information.As a result, the present embodiment 1 offers an advantage of being ableto reduce the transmission collision probability in the combination ofthe particular mobile stations, and to reduce the interference betweenthe mobile stations.

According to the present embodiment 1, the base station changes theerror correcting encoding ratio of the data channel, which is used inconjunction with the DPDCH in the downlink, in accordance with thequality information. As a result, the present embodiment 1 offers anadvantage of being able to reduce the transmission collision probabilityin the combination of the particular mobile stations, and to reduce theinterference between the mobile stations.

Embodiment 2

In the present embodiment 2, the maximum value of k is determined suchthat it differs from the least common multiple of any two k values lessthan the maximum value such as 53 of the k={0, 1, 5, 11, . . . , 53}.Thus, the collision probability reduces up to the maximum k value.

Furthermore, the maximum value of k is made less than the least commonmultiple of the two k values less than the maximum value except for 0and 1, such as 53 of the k={0, 1, 5, 11, 53} is less than 55, the leastcommon multiple of 5 and 11. Thus, as for two mobile stations assignedtwo k's (other than 0 and 1), the collision report cycle becomes greaterthan the maximum value of the k, thereby being able to reduce theprobability of the collision between the QI transmission.

In the present embodiment 2, the value k is determined considering theconditions of the foregoing embodiment 1. Thus, it can positively reducethe probability of the collision between the QI transmission.

As described above, the communication system of the present embodiment 2is configured such that the mobile stations (2) transmit to the basestation (1) the quality information (QI) about the downlink (3) from thebase station (1) to the mobile stations (2) at alterable report cycles(k), and the communication system includes the channel (5) that variesthe transmission rate by changing the transmission format of the datatransmitted from the base station (1) through the downlink (3) accordingto the quality information (QI) transmitted, wherein the individualreport cycles (k) of the mobile stations (2) are selected from a groupconsisting of 0, 1 and positive integers equal to or greater than two,where the maximum value of the positive integers differs from the leastcommon multiple of any two integers of the positive integers other thanthe maximum value.

In the communication system of the present embodiment 2, the maximumvalue is less than the least common multiple.

As is clear from the description above, according to the presentembodiment 2, the report cycles k of the mobile stations in thecombination of particular mobile stations are selected from 0, 1 andpositive integers equal to or greater than two, and the maximum value ofthe positive integers is made different from the least common multipleof any two integers of the positive integers other than the maximumvalue. As a result, the present embodiment 2 offers an advantage ofbeing able to reduce the transmission collision probability up to themaximum value of the k.

According to the present embodiment 2, the maximum value of the positiveintegers is made less than the least common multiples of any twopositive integers other than the maximum value. As a result, thecollision report cycle of the two mobile stations becomes greater thanthe maximum value of the k, which offers an advantage of being able toreduce the probability of the collision between the QI transmission.

Embodiment 3

In the present embodiment 3, the relations about the possible k values(other than 0 or 1) are specified that larger k values are obtained fromsmaller k values, and that the larger k values each have the relation of“the least common multiple of smaller two k values plus one”.Considering such k values, the k takes the values 0, 1, 2, 3, 5, 7, 11,15, 16, 22, 23, 31, 33, 34, 49, . . . , which are similar to the “valueswithout having the relation of a multiple” as specified in the foregoingembodiment 1. Accordingly, the present embodiment 3 can reduce theprobability of the collision between the QI transmission of theparticular mobile stations.

In addition, setting a unique relation between the smaller k values andthe larger k values makes it possible to obtain the larger k's from thesmaller k's, and hence to obtain the larger values as needed. Thisoffers an advantage of being able to eliminate the need for storing allthe possible numbers of k in the base station when there are many kvalues.

Although the present embodiment 3 takes an example of “(the least commonmultiple of two smaller k's)+1”, this is not essential. For example, itis obvious that other similar relationships between the k values arepossible, such as the relation “(the least common multiple of twosmaller k's)+3”.

As described above, the communication system of the present embodiment 3is configured such that the mobile stations (2) transmit to the basestation (1) the quality information (QI) about the downlink (3) from thebase station (1) to the mobile stations (2) at alterable report cycles(k), and the communication system includes the channel (5) that variesthe transmission rate by changing the transmission format of the datatransmitted from the base station (1) through the downlink (3) accordingto the quality information (QI) transmitted, wherein the individualreport cycles (k) of the mobile stations (2) are selected from 0, 1 andpositive integers equal to or greater than two, and the positiveintegers are obtained in such a manner that the larger values areobtained from the smaller values.

As is clear from the description above, according to the presentembodiment 3, the report cycles k of the mobile stations in thecombination of particular mobile stations are selected from 0, 1 andpositive integers equal to or greater than two, and the larger valuesare obtained from the smaller values. As a result, the presentembodiment 3 offers an advantage of being able to reduce the probabilityof the collision between the QI transmission of particular mobilestations, and to eliminate the need for storing all the possible numbersof k in the base station when there are many k values.

Embodiment 4

FIG. 9 is a diagram showing a communication system of an embodiment 4 inaccordance with the present invention. In FIG. 9, reference numerals 1a, 1 b and 1 c each designate a base station, 10 a, 10 b and 10 c eachdesignate a communication area (cell) of each of the base stations 1 a,1 b and 1 c, and 2 a and 2 b each designate a mobile station. Thereference numeral 20 designates an inter-base station communicationline, and reference numerals 6 a and 6 b each designate a HS-DPCCHtransmission from each of the mobile stations 2 a and 2 b.

In FIG. 9, only the uplinks 6 (6 a and 6 b: HS-DPCCH transmission) fromthe mobile stations 2 to the base stations 1 are shown among the links(channels) between the base stations 1 and mobile stations 2 to simplifythe explanation.

Next, the operation will be described.

The foregoing embodiments 1-3 describe the method of selecting the kvalues associated with the QI transmission timing control for a singlebase station. In contrast, the present embodiment 4 considers a casewhere a plurality of base stations are present, and the cells overlapwith each other.

Generally, the base stations are installed such that the cells overlapwith each other to prevent interruption of communication. In this case,if a plurality of mobile stations 2 a and 2 b carry out the QItransmission to the different base stations 1 a and 1 b in the areaswhere the cells overlap as shown in FIG. 9, the probability of thetransmission collision increases when the group of the possible k valuesis the same, and the interference between the mobile stations increases.

In this case, the base stations exchange information about the possiblenumbers of k with each other via the inter-base station communicationline 20, and use different groups of k. This makes it possible to reducethe probability of the collision between the QI transmission, and toreduce the interference between the mobile stations at the same time.

In particular, as for the smaller k that can readily cause thecollision, the base stations specify the different values.

As an extreme case, for example, consider the case where the basestations change the smallest k value other than 0 and 1, such as thebase station 1 a employs k={0, 1, 5, 11, 21, . . . }, the base station 1b uses k={0, 1, 6, 11, 21, . . . }, and the base station 1 c employsk={0, 1, 7, 11, 21, . . . }. In this case, the base stations as a wholecan reduce the probability of the collision between the QI transmission,and the interference between the mobile stations.

As a method of changing the possible numbers of k for the individualbase stations, it is possible to use the values based on therelationships described in the foregoing embodiment 3. Specifically, thevalues can be set such as “(the least common multiple of two smallerk's)+1”, “(the least common multiple of two smaller k's)+2”, and “(theleast common multiple of two smaller k's)+3”.

In addition, although the present embodiment 4 notifies the basestations of the groups of the k values via the inter-base stationcommunication line 20, other methods can also be used. For example, theindividual base stations broadcast information about the k values, andother base stations receive the information, so that the individual basestations set the different groups of k values on an autonomous basis.

As described above, the communication system of the present embodiment 4is configured such that the mobile stations (2) transmit to the basestations (1) the quality information (QI) about the downlinks (3) fromthe base stations (1) to the mobile stations (2) at alterable reportcycles (k), and the communication system includes the channel (5) thatvaries the transmission rate by changing the transmission format of thedata transmitted from the base stations (1) through the downlinks (3)according to the quality information (QI) transmitted, wherein theindividual base stations (1) receive the quality information (QI) fromthe mobile stations (2) at the report cycles (k) whose possible valuesdiffer from each other.

In the communication system of the present embodiment 4, the basestations (1) each exchange the report cycles (k), at which the basestations receive the quality information (QI) from the mobile stations(2), via the inter-base station communication line (20) connecting thebase stations (1) each.

As is clear from the description above, the present embodiment 4 isconfigured such that the base stations exchange the information aboutthe possible numbers of k with each other, and use different groups of kfrom each other. As a result, the present embodiment 4 offers anadvantage of being able to reduce the probability of the collisionbetween the QI transmission, and to reduce the interference between themobile stations at the same time.

The present embodiment 4 is configured such that the report cycle k istransmitted via the inter-base station communication line connecting theindividual base stations. As a result, using the different groups of koffers an advantage of being able to reduce the probability of thecollision between the QI transmission, and to reduce the interferencebetween the mobile stations at the same time.

INDUSTRIAL APPLICABILITY

As described above, the communication system in accordance with thepresent invention is suitable for the communication system in which aplurality of mobile stations are present for a base station, and for thecommunication system and the like in which mobile stations are presentat a distance of a base station.

1. A mobile station configured to transmit downlink quality informationto a base station, the mobile station comprising: a receiving unitconfigured (a) to receive a transmission cycle which determinestransmission timing of the downlink quality information, thetransmission cycle is selected based on a set including 0, 1, at leasttwo positive integers having no multiple relationship to each other, andat least two positive integers having a multiple relationship to eachother and being equal to or larger than the two positive integers havingno multiple relationship, and (b) to receive high-speed packet datatransmitted from the base station using a high-speed packet datachannel; and a transmitting unit configured (a) to transmit, to the basestation using a control channel, a response signal associated with thehigh-speed packet data received by the receiving unit, and (b) totransmit, to the base station using the control channel, the downlinkquality information in a subframe where a domain for the response signaland a domain for the downlink quality information are provided inseparate data fields of the subframe, wherein the downlink qualityinformation is transmitted by the transmitting unit in accordance withthe transmission cycle received by the receiving unit.
 2. A mobilestation configured to transmit downlink quality information to a basestation, the mobile station comprising: a receiving unit configured toreceive a transmission cycle which determines transmission timing of thedownlink quality information, the transmission cycle is selected basedon a set including 0, 1, at least two positive integers having nomultiple relationship to each other, and at least two positive integershaving a multiple relationship to each other and being equal to orlarger than the two positive integers having no multiple relationship; adownlink quality information obtaining unit configured to obtain anumerical value tabulated with a modulation method for a channel usedfor HSDPA (High Speed-Downlink Packet Access) based on a CPICH (CommonPilot Channel); and a transmitting unit configured (a) to transmit aresponse signal associated with a reception result of the channel usedfor HSDPA using a HS-DPCCH (High Speed Dedicated Physical ControlChannel), and (b) to transmit the numerical value obtained by thedownlink quality information obtaining unit using the HS-DPCCH inaccordance with the transmission cycle received by the receiving unit.3. A communication method for transmitting downlink quality informationto a base station, the communication method comprising the steps of:receiving a transmission cycle which determines transmission timing ofthe downlink quality information, the transmission cycle selected basedon a set including 0, 1, at least two positive integers having nomultiple relationship to each other, and at least two positive integershaving a multiple relationship to each other and being equal to orlarger than the two positive integers having no multiple relationship;receiving high-speed packet data transmitted from the base station usinga high-speed packet data channel; transmitting, to the base stationusing a control channel, a response signal associated with thehigh-speed packet data; and transmitting, to the base station using thecontrol channel, the downlink quality information in a subframe where adomain for the response signal and a domain for the downlink qualityinformation are provided in separate data fields of the subframe,wherein the transmitting downlink quality information step is performedin accordance with the transmission cycle received by the receiving atransmission cycle step.
 4. A communication method for transmittingdownlink quality information to a base station, the communication methodcomprising the steps of: receiving a transmission cycle which determinestransmission timing of the downlink quality information, thetransmission cycle selected based on a set including 0, 1, at least twopositive integers having no multiple relationship to each other, and atleast two positive integers having a multiple relationship to each otherand being equal to or larger than the two positive integers having nomultiple relationship; obtaining as downlink quality information anumerical value tabulated with a modulation method for a channel usedfor HSDPA (High Speed-Downlink Packet Access) based on a CPICH (CommonPilot Channel); transmitting a response signal associated with areception result of the channel used for HSDPA using an HS-DPCCH (HighSpeed Dedicated Physical Control Channel); and transmitting thenumerical value obtained by the obtaining step using the HS-DPCCH inaccordance with the transmission cycle received by the receiving atransmission cycle step.
 5. A base station configured to receivedownlink quality information transmitted from a mobile station, the basestation comprising: a first transmitting unit configured to transmithigh-speed packet data to a mobile station using a high-speed packetdata channel for downlink; a second transmitting unit configured totransmit, to the mobile station, a transmission cycle selected based ona set including 0, 1, at least two positive integers having no multiplerelationship to each other, and at least two positive integers having amultiple relationship to each other and being equal to or larger thanthe two positive integers having no multiple relationship; and areceiving unit configured (a) to receive the downlink qualityinformation transmitted by the mobile station through HSDPCCH, and (b)to receive a response signal associated with the high-speed packet datareceived by the mobile station, wherein the downlink quality informationis received via a control channel in a subframe where a domain for theresponse signal and a domain for the downlink quality information areprovided in separate data fields of the subframe, and wherein thedownlink quality information is transmitted from the mobile station inaccordance with the transmission cycle.
 6. A base station configured toreceive downlink quality information transmitted from a mobile station,the base station comprising: a first transmitting unit configured totransmit high-speed packet data to a mobile station through a channelfor HSDPA; a second transmitting unit configured to transmit to themobile station a transmission cycle selected based on a set including 0,1, at least two positive integers having no multiple relationship toeach other, and at least two positive integers having a multiplerelationship to each other and being equal to or larger than the twopositive integers having no multiple relationship; and a receiving unitconfigured (a) to receive the downlink quality information transmittedby the mobile station through HSDPCCH, the downlink quality informationobtained by the mobile station based on a CPICH (Common Pilot Channel)is one of numeric values tabulated with modulation methods for thechannel for the HSDPA, and (b) to receive a response signal associatedwith the high-speed packet data received by the mobile station, whereinthe downlink quality information is transmitted from the mobile stationin accordance with the transmission cycle.
 7. A communication method forreceiving downlink quality information transmitted from a mobilestation, the communication method comprising the steps of: transmittinghigh-speed packet data to a mobile station through a high-speed packetdata channel for downlink; transmitting, to the mobile station, thetransmission cycle selected based on a set including 0, 1, at least twopositive integers having no multiple relationship to each other, and atleast two positive integers having a multiple relationship to each otherand being equal to or larger than the two positive integers having nomultiple relationship; receiving the downlink quality informationtransmitted by the mobile station through HSDPCCH; and receiving aresponse signal associated with the high-speed packet data received bythe mobile station, wherein the downlink quality information is receivedvia a control channel in a subframe where a domain for the responsesignal and a domain for the downlink quality information are provided inseparate data fields of the subframe, and the downlink qualityinformation is transmitted from the mobile station in accordance withthe transmission cycle.
 8. A communication method for receiving downlinkquality information transmitted from a mobile station, the communicationmethod comprising the steps of: transmitting high-speed packet data to amobile station through a channel for HSDPA; transmitting, to the mobilestation, a transmission cycle selected based on a set including 0, 1, atleast two positive integers having no multiple relationship to eachother, and at least two positive integers having a multiple relationshipto each other and being equal to or larger than the two positiveintegers having no multiple relationship; and receiving the downlinkquality information transmitted by the mobile station through HSDPCCH,the downlink quality information obtained by the mobile station based onCPICH (Common Pilot Channel) is one of numeric values tabulated withmodulation methods for the channel for the HSDPA; and receiving aresponse signal associated with the high-speed packet data received bythe mobile station, wherein the downlink quality information istransmitted from the mobile station in accordance with the transmissioncycle.
 9. A mobile station configured to transmit downlink qualityinformation to a base station, the mobile station comprising: areceiving unit configured to receive high-speed packet data transmittedfrom the base station using a high-speed packet data channel; and atransmitting unit configured (a) to transmit a response signalassociated with the high-speed packet data received by the receivingunit, and (b) to transmit the downlink quality information in a subframewhere a domain for the response signal and a domain for the downlinkquality information are separately provided in separate data fields ofthe subframe, wherein the transmitting unit transmits the downlinkquality information under the timing control based on a transmissioncycle included in a set which includes 0, 1, at least two positiveintegers having no multiple relationship to each other, and at least twopositive integers having a multiple relationship to each other and beingequal to or larger than the two positive integers having no multiplerelationship.
 10. A mobile station configured to transmit downlinkquality information to a base station, the mobile station comprising: areceiving unit configured to receive high-speed packet data transmittedfrom the base station using a high-speed packet data channel; a downlinkquality information obtaining unit configured to obtain a numericalvalue tabulated with a modulation method for a channel used for HSDPA(High Speed-Downlink Packet Access) based on a CPICH (Common PilotChannel); and a transmitting unit configured (a) to transmit a responsesignal associated with a reception result of the channel used for HSDPAusing an HS-DPCCH (High speed Dedicated Physical Control Channel), and(b) to transmit the numerical value obtained by the downlink qualityinformation obtaining unit using the HS-DPCCH, in accordance with atransmission cycle, wherein the transmitting unit transmits the downlinkquality information under the timing control based on the transmissioncycle included in a set which includes 0, 1, at least two positiveintegers having no multiple relationship to each other, and at least twopositive integers having a multiple relationship to each other and beingequal to or larger than the two positive integers having no multiplerelationship.
 11. A communication method for transmitting downlinkquality information to a base station, the communication methodcomprising the steps of: receiving high-speed packet data transmittedfrom the base station using a high-speed packet data channel; andtransmitting a response signal associated with the high-speed packetdata received in the receiving step; transmitting the downlink qualityinformation in a subframe where a domain for a response signal,associated with the high-speed packet data, and a domain for thedownlink quality information are provided in separate data fields of thesubframe, and wherein a transmission of the downlink quality informationis controlled based on a transmission cycle included in a set whichincludes 0, 1, at least two positive integers having no multiplerelationship to each other, and at least two positive integers having amultiple relationship to each other and being equal to or larger thanthe two positive integers having no multiple relationship.
 12. Acommunication method for transmitting downlink quality information to abase station, the communication method comprising the steps of:receiving high-speed packet data transmitted from the base station usinga high-speed packet data channel; obtaining as the downlink qualityinformation a numerical value tabulated with a modulation method for achannel used for HSDPA (High Speed-Downlink Packet Access) based on aCPICH (Common Pilot Channel); transmitting a response signal associatedwith a reception result of the channel used for HSDPA using an HS-DPCCH(High Speed Dedicated Physical Control Channel); and transmitting thenumerical value obtained by the obtaining step using the HS-DPCCH inaccordance with a transmission cycle, wherein a transmission of thedownlink quality information is controlled based on the transmissioncycle included in a set which includes 0, 1, at least two positiveintegers having no multiple relationship to each other, and at least twopositive integers having a multiple relationship to each other and beingequal to or larger than the two positive integers having no multiplerelationship.
 13. A base station configured to receive downlink qualityinformation transmitted from a mobile station, the base stationcomprising: a transmitting unit configured to transmit high-speed packetdata to a mobile station using a high-speed packet data channel fordownlink; and a receiving unit configured (a) to receive the downlinkquality information transmitted by the mobile station through HSDPCCH inaccordance with a transmission cycle, and (b) to receive a responsesignal associated with the high-speed packet data received by the mobilestation, wherein the downlink quality information is received via acontrol channel in a subframe where a domain for the response signal anda domain for the downlink quality information are provided in separatedata fields of the subframe, and the receiving unit is furtherconfigured to receive the downlink quality information which istransmitted from the mobile station under the timing control based onthe transmission cycle included in a set which includes 0, 1, at leasttwo positive integers having no multiple relationship to each other, andat least two positive integers having a multiple relationship to eachother and being equal to or larger than the two positive integers havingno multiple relationship.
 14. A base station configured to receivedownlink quality information transmitted from a mobile station, the basestation comprising: a transmitting unit configured to transmithigh-speed packet data to a mobile station through a channel for HSDPA;a receiving unit configured (a) to receive the downlink qualityinformation transmitted by the mobile station through HSDPCCH inaccordance with a transmission cycle, and (b) to receive a responsesignal associated with the high-speed packet data received by the mobilestation, wherein the downlink quality information is a numeric valuetabulated with modulation methods for the channel for the HSDPA andobtained by the mobile station based on a CPICH (Common Pilot Channel),and the receiving unit receives the downlink quality information whichis transmitted from the mobile station under the timing control based onthe transmission cycle included in a set which includes 0, 1, at leasttwo positive integers having no multiple relationship to each other, andat least two positive integers having a multiple relationship to eachother and being equal to or larger than the two positive integers havingno multiple relationship.
 15. A communication method for receivingdownlink quality information transmitted from a mobile station, thecommunication method comprising the steps of: transmitting high-speedpacket data to a mobile station through a high-speed packet data channelfor downlink; receiving the downlink quality information transmitted bythe mobile station through HSDPCCH in accordance with a transmissioncycle; and receiving a response signal associated with the high-speedpacket data received by the mobile station, wherein the downlink qualityinformation is received via a control channel in a subframe where adomain for the response signal and a domain for the downlink qualityinformation are provided in separate data fields of the subframe, and atransmission of the downlink quality information is controlled based onthe transmission cycle included in a set which includes 0, 1, at leasttwo positive integers having no multiple relationship to each other, andat least two positive integers having a multiple relationship to eachother and being equal to or larger than the two positive integers havingno multiple relationship.
 16. A communication method for receivingdownlink quality information transmitted from a mobile station, thecommunication method comprising the steps of: transmitting high-speedpacket data to a mobile station through a channel for HSDPA; receivingthe downlink quality information transmitted by the mobile stationthrough HSDPCCH in accordance with a transmission cycle; and receiving aresponse signal associated with the high-speed packet data received bythe mobile station, wherein the downlink quality information is anumeric value tabulated with modulation methods for the channel for theHSDPA and obtained by the mobile station based on a CPICH (Common PilotChannel), and a transmission of the downlink quality information iscontrolled based on the transmission cycle included in a set whichincludes 0, 1, at least two positive integers having no multiplerelationship to each other, and at least two positive integers having amultiple relationship to each other and being equal to or larger thanthe two positive integers having no multiple relationship.